a simple question
1. Why x/∞=0 for x real numbers. can you explain it?
2.why x/0 for x real numbers is infinity (∞)?

STOP COPY PASTE THIS IS NOT A SERIOUS QUESTION BUT BECAUSE I AM CURIOUS!
DON'T ANSWER JUST FOR A POINTS BUT TO HELP PEOPLE!​

Answers

Answer 1

Neither of these statements are true.

x/∞ = 0 is a nonsensical statement. It's more accurate to say

[tex]\displaystyle \lim_{y\to\infty} \frac xy = 0[/tex]

for any real number x. The important bit is that y is an arbitrarily large number as it approaches ∞. To convince yourself that this expression approaches 0 as y gets larger and larger, try fixing x and pick any increasing sequence of numbers for y.

For example, let x = 1 and take y from the sequence of increasing powers of 10, {10, 10², 10³, …}, which grows without bound. Then

1/10 = 0.1

1/10² = 0.01

1/10³ = 0.001

and so on. Naturally, the larger the power of 10 and thus the larger y gets, the closer x/y gets to 0.

Similarly, x/0 is nonsense, but the "limit-ized" version of the claim is also incorrect. For any fixed real number x, the limit

[tex]\displaystyle \lim_{y\to0} \frac xy[/tex]

does not exist. Suppose x > 0. If y approaches 0 from above, then y > 0 and x/y > 0 and

[tex]\displaystyle \lim_{y\to0^+} \frac xy = +\infty[/tex]

which you can convince yourself is true by reversing the example from before. Let x = 1 and take y from the sequence of decreasing powers of 10, {1/10, 1/10², 1/10³, …}, which converges to 0. Then

1/(1/10) = 10

1/(1/10²) = 100

1/(1/10³) = 1000

and so on. The smaller y gets (while still being positive), the larger x/y becomes.

But now suppose y < 0 and that y approaches 0 from below. Then x/y < 0, and

[tex]\displaystyle \lim_{y\to0^-} \frac xy = -\infty[/tex]

The limits from either side do not match, so the limit as y approaches 0 does not exist.

You can use the same reasoning for when x < 0.

The case of x = 0 is special, however. Since y is approaching 0, it's never actually the case that y = 0. 1/y is then some non-zero real number, and multiplying it by x = 0 makes x/y = 0. Then

[tex]\displaystyle \lim_{y\to0} \frac 0y = 0[/tex]

So in general,

[tex]\displaystyle \lim_{y\to0} \frac xy = \begin{cases}0 & \text{if }x = 0 \\ \text{does not exist} & \text{otherwise}\end{cases}[/tex]


Related Questions

30 divided by 5 - 2 + 7 = 3
Then , write down the correct equation.

Answers

Answer:

30 : (5 - 2 + 7) = 3

Step-by-step explanation:

30 divided by 5 - 2 + 7 = 3

Then , write down the correct equation.

30 : (5 - 2 + 7) = 3

30 : (3 + 7) = 3

30 : 10 = 3

3 = 3

The answer is 3 I’m pretty sure

Solve for all values of y in simplest form.
21 = |7y|
Answer: y =
Submit Answer

Answers

Answer: y= ±3

Explanation: 21/7=3 BUT the absolute sign mean no matter whats inside the sign the outcome will always be positive afterwards , so it can be a positive or negative 3.

I’m struggling to answer this can someone please help me I would highly appreciate it

Answers

Answer:

Not similar

Step-by-step explanation:

If you have scratch paper, its best to label the angles and sides given. You can also rotate the orientation of one of the triangles if that helps visually.

First lets look at the sides.

Notice the common factor between side AB and side XY.

14/7=2

Notice the common factor between side AC and side XZ.

22/11=2

So far so good right? Well, IF these triangles are similar, that means that angle X must correspond to angle A. Since corresponding angles of similar triangles are equal to each other, lets check of angle X is equal to angle A.

Angle X = 29 degrees

Angle A = 28 degrees

28 does not equal 29 degrees. Therefore, the triangles are not similar. If angles X and A were equal, than the triangles would have been similar due to the Side-Angle-Side rule (SAS).

find the slope of the line
x-intercept is twice as y-intercept​

Answers

Answer:

-1/2

Step-by-step explanation:

It mentions that the x-intercept is equal to twice the y-intercept.

=============================================================

Let :

⇒ x-intercept = (2a, 0)

⇒ y-intercept = (0, a)

==============================================================

Slope formula :

m = y₂ - y₁ / x₂ - x₁

=============================================================

Solving :

⇒ m = a - 0 / 0 - 2a

⇒ m = a / -2a

⇒ m = -1/2

4 divided by 5/7 in its mixed form and simplest form

Answers

[tex]4\div\cfrac{5}{7}\implies \cfrac{4}{1}\div\cfrac{5}{7}\implies \cfrac{4}{1}\cdot \cfrac{7}{5}\implies \cfrac{28}{5}\implies 5\frac{3}{5}[/tex]

Kenji is using walnuts to bake muffins and granola for his restaurant. each batch of muffins
1
pound of walnuts. he needs 2 pounds of walnuts to make granola. kenji can use up
2
to 8 pounds of walnuts and still have enough for baking tomorrow.
uses
let b represent the number of batches of muffins kenji makes.
write an inequality that represents the situation.

Answers

Answer:

Step-by-step explanation:

1/2b + 2 ≤ 8

b ≤ 12

Answer:

Step-by-step explanation:

1.1 How many grams of can of apple pie filling Chantel is going to use in the Apple (2) Cinnamon Cake.​

Answers

The number of grams of canned apple that Chantel needs for her apple-cinnamon cake is about 1400 grams.

How to calculate the amount of canned apple that Chantel needs?

To know the amount of canned apple that Chantel needs for her apple and cinnamon cake recipe, we must review the amount of apple that she needs for the filling of her cake.

According to the basic recipe to make this cake, we need 6 to 8 apples. Taking into account that each apple weighs about 200g, we can infer that Chantel is going to use about 1400g of canned apple as shown below.

On average we need 7 apples.

6 + 8 = 1414 ÷ 2 = 7

Each apple weighs 200g, so 7 apples would be 1400g.

7 × 200g = 1400g

Based on the above, Chantel needs 1400g of canned apple.

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Maria's car has a gas mileage of 31 miles per gallon. How many miles can Maria travel on 9 gallons of gas?

Answers

Answer:

279 miles

Step-by-step explanation:

31 miles/gal  *  9 gallons = 279 miles

The graph of an absolute value function contains the points (–3, 5), (0, 2) and (3, 5). Which could be the function represented by this graph? Check all that apply.

f(x) = |x| + 2
f(x) = –|x| + 2
f(x) = |x| – 2
f(x) = |–x + 2|
f(x) = |–x| + 2
f(x) = –|x| – 2
f(x) = |x + 2|

Answers

The absolute value functions that contains the points are:

f(x) = |x| + 2f(x) = |-x| + 2

Which could be the function represented by this graph?

Here we have the points (-3, 5), (0, 2), and (3, 5). We want to see which ones of the given functions have that points.

To check that, we need to evaluate the functions in the first value of each point and see if the outcome is the second value of the correspondent point.

For example, for the first equation:

f(-3) = |-3| + 2 = 5   so it has the point (-3, 5)f(0) = |0| + 2 = 2  so it has the point (0, 2)f(3) = |3| + 2 = 5  so it has the point (3, 5).

The other option that also contains these 3 points is:

f(x) = |-x| + 2

f(-3) = |3| + 2 = 5  so it has the point (-3, 5)f(0) = |-0| + 2 = 2  so it has the point (0, 2)f(3) =  |-3| + 2 = 5  so it has the point (3, 5).

And all the other options can be trivially discarded (by evaluating them).

So the two correct options are:

f(x) = |x| + 2f(x) = |-x| + 2

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Name the types of angles shown.
L
M
Check all that apply.
A. straight angle
B. right angle
c. supplementary angles
D. complementary angles

Answers

Answer:

Ans : A. Straight angle

Step-by-step explanation:

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Brain

a.) Find h(g(x)) if
h(x)= 2x+9
and
g(x) = 4*

Answers

Answer:

h(4)=17

Step-by-step explanation:

h(g(x)), h(x)= 2x+9; g(x)=4

2(4)+9= 8+9=17

A rectangular shop in the mall is 10 meters long and 6 meters wide. what is its area?

Answers

Step-by-step explanation:

the area of a rectangle is

length × width

I am sure you discussed and learned this in class, otherwise you would not get such a problem to solve.

it is a really simple thing : just multiply the 2 numbers.

the area of the shop is

10 × 6 = 60 m²

the really important thing is not to forget that the result is not measured in meters, as this is no longer just a 1- dimensional length. since we multiplied two meter lengths, it is measured in square meters, which are squares of 1 meter side length, and we say how many such squares fit into the area.

Danny attempted to complete a 500 piece puzzle. By the end of the night, he places p pieces in the puzzle correctly, which expression shows how many more pieces he needs to add to the puzzle to complete it

Answers

The expression that shows how many more pieces he needs to add to the puzzle to complete it is 500 - p

How to determine the expression?

The given parameters are:

Total = 500

Correct = p

The remaining piece is calculated using:

Total =Correct + Remaining

Substitute known values

p + Remaining = 500

Subtract p from both sides

Remaining = 500 - p

Hence, the expression is 500 - p

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If you place a 39-foot ladder against the top of a building and the bottom of the ladder is 33 feet from the building how tall is the building?

Answers

Answer:

Formulate

Based on the given conditions, formulate:

[tex] \sqrt{3 {9}^{2} } - 3 {3}^{2} [/tex]

Evaluate

Evaluate the equation/expression:

20.78461

SO THE ANSWER IS 20.78461

Answer:

20.78 feet

Step-by-step explanation:

[tex]39^{2} =h^{2} +33^{2} \\1521= h^{2} +1089\\h^{2}= 1521-1089\\h^{2} =432h= 20.78[/tex]

someone help please

Answers

Answer:

I think 40.

Step-by-step explanation:

annie has some sweets. teddy gives her some sweets and she now has 50% more . rosie gives her some sweets and she now has an extra 40% . annie now has 63 sweets. how many did she have originally

Answers

Using proportions, considering the amount she received from each person, it is found that Annie had 30 sweets originally.

What is a proportion?

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, we have that:

Initially, she had n sweets.With the ones she got from Teddy, the amount became 1.5n.With the amount from Rosie, the amount became 1.4 x 1.5 x n.

The final amount was of 63, hence:

1.4 x 1.5 x n = 63

n = 63/(1.4 x 1.5)

n = 30.

Annie had 30 sweets originally.

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Which of the following shows how to calculate the probability of randomly selecting a cat or dog?
P(cat) + P(dog)
P(cat) − P(dog)
P(cat) · P(dog)
P(cat) ÷ P(dog)

Answers

The probability of randomly selecting a cat or dog is P(cat or dog) = P(cat) + P(dog)

Since we cannot select a cat and dog at the same time, their probabilities are mutually exclusive

Probability of mutually exclusive events

If we have events a and b which are mutually exclusive with probabilities P(a) and P(b) respectively, the probability of a or b is P(a or b) = P(a) + P(b)

Probability of randomly selecting a cat or dog

Let

P(cat) = probability of selecting a cat and P(dog) = probability of selecting a dog

So, probability of randomly selecting a cat or dog is

P(cat or dog) = P(cat) + P(dog)

So, probability of randomly selecting a cat or dog is P(cat or dog) = P(cat) + P(dog)

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What is the value of x?

Answers

the answer is 120. ur welcome
Answer: x=138

Explanation: an octagons interior angle sum is 1080 . if you add the given interior angles then subtract the total from 1080 , you will result in 138 .

Which of the following is not a triangle congruence theorem?

AAA
AAS
ASA

Answers

Answer:

A. (AAA)

Step-by-step explanation:

.....(AAA) "does not work because it can produce similar but not congruent triangles"

.....(AAS) "If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent."

.....(ASA)"triangles are congruent if any two angles and their included side are equal in the triangles."

Hope This Helped

Alison is buying binders for school. Small binders cost $3 each, and large binders cost $5 each. If Alison needs to buy at least 12 binders and has no more than $45 to spend, what is the maximum number of large binders she can buy?

a. 4

b 5

c 8

d 9

Answers

Answer:

9

Step-by-step explanation:

Answer:

4 large folders     ( and 8 small folders....with $ 1 left over)

Step-by-step explanation:

x = small    y = large folders

x+y >= 12      x >= 12-y

3x + 5y <= 45

3 (12-y) + 5y <=45

36 -3y + 5y <= 45

    y <= 4.5               you cannot buy .5 of a large folder, so 4 large folders

What is the answer to (2 * 6)^3/2?

Answers

Answer:

864

Step-by-step explanation:

First, you multiply 2 and 6, so it's 12, and multiply it by 144, so it's 1728, and divide it by 2. Therefore, it's 864!

The coordinates (1, 1), (1, 3), (3, 3), and (x, y) form a square when graphed on a coordinate plane. Which ordered pair would be the fourth vertex of the square? A (3, 1) B (1,3) C (3,5) D (3, 0
)​

Answers

Answer:

3,1

....................................

Help please

1.In ∆ABC, how many triangles are formed given: a=10 cm, b=18 cm, c=105°?

A. 1
B. 2
C. 3
D. None

2. In ∆ABC, if <A is obtuse and a<c, then how many triangle/s can be formed?

A. 1
B.2
C. 3
D. None​

Answers

For questions 1 and 2 options, A and D are correct respectively.

What is the triangle?

A triangle is a three-sided polygon. It is one of the most fundamental geometric forms.

1. In ∆ABC,

a=10 cm, b=18 cm, c=∠105°

For the given data only one triangle is formed. Option A is correct.

2. In ∆ABC, if <A is obtuse and a<c,

An obtuse angle is an angle more than the 90°.The given condition is wrong. None of the triangle is formed from the given options.

Hence for questions 1 and 2 options A and D are correct respectively.

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Which angle in the figure is a right angle?

A. ∠STU

B. ∠TSR

C. ∠TUS

D. I don't know.

Answers

Answer:

∠TUS I'm pretty sure because t and u make a right angle

Karen needs to make a total of 60 deliveries this week. So far she has completed 33 of them What percentage of her total deliveries has Karen completed?

Answers

Answer:

55%

Step-by-step explanation:

(33/60) * 100

leave a comment if u need further explanation

how many whole weeks are in a year

Answers

Answer:

52 weeks are there in a year

Step-by-step explanation:

365/7

Question 10 solve for me please

Answers

Answer: D.

Step-by-step explanation:

x + 3 > 2       Original equation

x > -1             Subtract 3 on both sides

Number line that has an open circle and on -1 that goes right = D.

Which intervals show f(x) decreasing?

Answers

Oh nah that’s why I’m saying that you didn’t mean to me like that too but I just got a message saying it was okay but I’m just okay I just woke up him and I went


A cube has side length 3 inches. A sphere has a radius of
3 inches. (Lesson 5-16)
a. Before doing any calculations, predict which solid has greater surface
area to volume ratio.
b. Calculate the surface area, volume, and surface area to volume ratio for
each solid.

Answers

I predict that the solid with the  greater surface area to volume ratio would be the cube.

The volume of the cube is 27in³

The surface area of the cube is

The ratio of surface area to volume for the cube is 2.

The volume of the sphere is 113.14 in³

The surface area of the sphere is 113.14 in²

The ratio of surface area to volume is 1.

What is the surface area and volume of each solid?

The volume of a cube = side length³

3³ = 27 in³

The surface area of a cube = 6a²

a = side length

6 x (3²) = 54 inches²

Ratio of surface area to volume = 54 / 27 = 2

The volume of the sphere= 4/3πr³

4/3 x 22/7 x 3³ = 113.14 in³

The surface area of the sphere = 4πr²

4 x 22/7 x 3² = 113.14 in²

Ratio of surface area to volume = 113.14 / 113.14 = 1

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Find the area of each triangle. Round to the nearest tenth.

Answers

Answer:

A ≈ 9.6 units²

Step-by-step explanation:

the area (A) of the triangle is calculated as

A = product of 2 sides × sin (angle between them ) , that is

A = 3 × 5 × sin40° = 15 × sin40° ≈ 9.6 units² ( to the nearest tenth )

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